The zero-information-limit condition and spurious inference in weakly identified models

In many econometric models the asymptotic variance of a parameter estimate depends on the value of another structural parameter in such a way that the data contain little information about the former when the latter is close to a critical value. This paper introduces the zero-information-limit-condition (ZILC) to identify such models where 'weak identification' leads to spurious inference. We find that standard errors tend to be underestimated in these cases, but the size of the asymptotic t-test may either be too great (the intuitive case emphasized in the 'weak instrument' literature) or too small as in two cases illustrated here.